If the locus of the foot of the perpendicular drawn from centre upon any tangent to the ellipse x 2 40 + y 2 10 = 1 is x 2 + y 2 2 = a x 2 + b y 2 , then a – b is equal to

Step-by-step solution

Slope of O P = k h ⇒ slope of the tangent is - h k Hence, the equation of tangent P Q is ( y - k ) x - h = - h k ⇒ y = - h k x + h 2 + k 2 k ⇒ h 2 + k 2 k 2 = 40 - h k 2 + 10 c o n d i t i o n o f ta n g e n c y is c 2 = a 2 m 2 + b 2 ⇒ x 2 + y 2 2 = 40 x 2 + 10 y 2 ⇒ a – b = 30